What is the least common multiple of 7 and 3?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 7 and 3. To solve this, we will identify the smallest number that is a multiple of both 7 and 3.
Answer
21
Answer for screen readers
The least common multiple of 7 and 3 is 21.
Steps to Solve
1. **Identify the multiples of each number**
List the first few multiples of 7 and 3.
Multiples of 7: 7, 14, 21, 28, 35, 42, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
2. **Find the smallest common multiple**
Identify the smallest number that appears in both lists of multiples.
21 is the smallest multiple that appears in both lists.
3. **Use the prime factorization method (optional)**
Another method to find the LCM is by using the prime factorization of each number.
7 is a prime number, so the prime factorization of 7 is 7^1.
3 is also a prime number, so the prime factorization of 3 is 3^1.
LCM is found by taking the highest power of each prime number in the factorization.
So, LCM(7, 3) = 7^1 * 3^1 = 21.
The least common multiple of 7 and 3 is 21.
More Information
The least common multiple (LCM) is the smallest non-zero common multiple of two or more numbers. It is often used in problems involving ratios or when adding and subtracting fractions with different denominators.
Tips
A common mistake is to stop before identifying the smallest multiple that appears in both lists, or to not list enough multiples to find the common one. It can also be easy to confuse the greatest common divisor (GCD) with the LCM.
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